subscripts of pi'a and sa'i

[phma]

Section 18.15 states "Matrices of more than two dimensions can be built up using either pi'a or sa'i with an appropriate subscript numbering the dimension." Which subscript is pi'a and which is sa'i?

[lagleki]

On Fri, Mar 19, 2021, 13:40 Pierre Abbat @.***> wrote:

Section 18.15 states "Matrices of more than two dimensions can be built up using either pi'a or sa'i with an appropriate subscript numbering the dimension." Which subscript is pi'a and which is sa'i?

It doesn't matter in case you describe dimension > 2.

Or are you asking whether sa'i= pi'axire?

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[phma]

Yes. It's not clear whether subscripts start at 0 or 1 or whether pi'a or sa'i has the smaller subscript. So it could be:

• pi'a=pi'axino, sa'i=pi'axipa
• sa'i=pi'axino, pi'a=pi'axipa
• pi'a=pi'axipa, sa'i=pi'axire
• sa'i=pi'axipa, pi'a=pi'axire.

[lagleki]

"numbering the dimension" implies vectors being of dimension 1 should have {xipa}. However, it might be beneficial to have {xi mlatu bu} form as an alternative. See https://pytorch.org/docs/stable/named_tensor.html

On Fri, Mar 19, 2021, 18:43 Pierre Abbat @.***> wrote:

Yes. It's not clear whether subscripts start at 0 or 1 or whether pi'a or sa'i has the smaller subscript. So it could be:

• pi'a=pi'axino, sa'i=pi'axipa
• sa'i=pi'axino, pi'a=pi'axipa
• pi'a=pi'axipa, sa'i=pi'axire
• sa'i=pi'axipa, pi'a=pi'axire.

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[lagleki]

@phma what do you think of this fix?

Matrices of more than two dimensions can be built up using either
      <valsi>pi'a</valsi>
      or
      <valsi>sa'i</valsi>
      with an appropriate subscript labeling the dimension. When subscripted, there is no difference between
      <valsi>pi'a</valsi>
      and
      <valsi>sa'i</valsi>. Labels can be any anything that <valsi>xi</valsi> supports, e.g. <valsi>pa</valsi> or <valsi>mlatu bu</valsi>.

[phma]

Still doesn't answer the question. Is {pi'a} equivalent to {pi'axino}, {pi'axipa}, or {pi'axire}? Likewise for {sa'i}?

[lagleki]

I dont think they are necessarily equivalent. Dimensions can be arbitrary labels.